Recently, sigma delta, or noise-shaping, analog-to-digital and digital-to-analog converters have come into widespread use. This type of converter uses a relatively coarse quantizer, usually a single bit, embedded in a feedback loop. The feedback loop causes the large quantization noise of the quantizer to become shaped in the frequency domain such that the noise over a small range of the spectrum is very low. The out-of-band noise is then removed by a digital filter in the case of an analog-to-digital converter, or an analog filter in the case of a digital-to-analog converter. Sigma delta converters exhibit excellent linearity and low quantization noise.
While early noise-shaping converters commonly used a one bit quantizer, multi-bit loop quantizers have recently received considerable attention. A multi-bit loop quantizer improves the performance of a sigma delta converter very significantly, especially with respect to signal-to-noise ratio, for a given oversampling ratio. The most serious drawback to multi-bit noise-shaping converters is that the matching of analog bit weights affects the linearity of the converter. The matching must be as good as the desired resolution of the converter. For example, a true 16-bit converter would require analog component matching to one part in 2.sup.16. Thus, one of the most important advantages of noise-shaping converters, namely that there is no requirement for precise analog component matching, is lost.
U.S. Pat. No. 5,404,142, issued Apr. 4, 1995 to Adams et al, discloses a noise-shaped scrambling technique that relieves the burden of tight analog component matching. The quantized noise-shaped word is first converted to a "thermometer code", where for an N-bit quantized word, 2 .sup.N equally-weighted elements are used. In the thermometer code, the number of output bits set to one is equal to the input value. The fact that the output bits are equally weighted allows dynamic mapping of digital input bits to analog elements of the digital-to-analog converter. By using an array of swapping elements whose state is controlled by the data itself, analog mismatch errors cause shaped noise to appear in the output spectrum. Therefore, most of the noise energy is outside the band of interest.
In this prior art technique, the required number of swapper cells is proportional to (M/2)*LOG.sub.2 (M) where M=2.sup.N, N being the number of bits used in the noise-shaping quantizer. For example, when a 4-bit word is converted to a 16-level thermometer code, the number of swapper cells is 8.multidot.4=32.
In many cases, it is desirable to use a large number of bits in the loop quantizer of the sigma delta converter. For example, using a larger number of bits in a digital-to-analog converter results in a smaller amount of out-of-band quantization noise. This in turn relaxes the requirement on the analog low pass filter that follows the converter. Unfortunately, using a large number of bits in the loop quantizer causes the area and power of the circuit, typically implemented as a monolithic integrated circuit, to grow to impractical levels. For example, a 6-bit loop quantizer would require a thermometer encoder having 64 output bits and a 64 element digital-to-analog converter, each of the elements being a capacitor, a current source or a voltage source.
Accordingly, it is desirable to provide a noise-shaping converter using a multi-bit quantizer, wherein the above drawbacks are alleviated.